Time taken by CO2 gas to diffuse 5000km distance is 2sec.Find the time taken by Cl2 gas to diffuse the same distance.
To find the time taken by Cl2 gas to diffuse the same distance as CO2, we can use Graham's Law of Diffusion. According to Graham's Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
First, we need to determine the molar masses of CO2 and Cl2. The molar mass of CO2 is calculated by adding the atomic masses of carbon (C) and two oxygen (O) atoms.
The atomic masses of carbon (C) and oxygen (O) are:
C: 12.01 g/mol
O: 16.00 g/mol
Hence, the molar mass of CO2 is:
Molar mass of CO2 = 12.01 g/mol + (16.00 g/mol × 2) = 44.01 g/mol
Now, let's determine the molar mass of Cl2:
The atomic mass of chlorine (Cl) is 35.45 g/mol.
Hence, the molar mass of Cl2 is:
Molar mass of Cl2 = 35.45 g/mol + 35.45 g/mol = 70.90 g/mol
Since the rates of diffusion are inversely proportional to the square root of the molar masses, we can set up the following equation:
(rate of CO2 gas) / (rate of Cl2 gas) = sqrt(molar mass of Cl2) / sqrt(molar mass of CO2)
Given that the time taken by CO2 gas to diffuse the distance is 2 seconds, we can take the rate of CO2 gas diffusion as 1/2 seconds.
Plugging in the values:
(1/2) / (rate of Cl2 gas) = √(70.90 g/mol) / √(44.01 g/mol)
Simplifying the equation, we get:
(rate of Cl2 gas) = (√(44.01 g/mol) / √(70.90 g/mol)) * (1/2)
Now, we can calculate the rate of Cl2 gas diffusion:
(rate of Cl2 gas) = (0.6635) * (1/2) ≈ 0.33175
Since we have the rate and the distance to be covered, we can use the formula:
distance = rate × time
To find the time taken by Cl2 gas to diffuse the same distance of 5000 km:
5000 km = 0.33175 × time
Rearranging the equation to solve for time:
time = 5000 km / 0.33175
Calculating the time:
time ≈ 15063.60 seconds
Therefore, according to Graham's Law of Diffusion, the time taken by Cl2 gas to diffuse the same distance of 5000 km is approximately 15063.60 seconds.
To find the time taken by Cl2 gas to diffuse the same distance as CO2 gas, we can use Graham's Law of Diffusion. According to Graham's Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
First, let's find the molar masses of CO2 and Cl2:
- Molar mass of CO2 (carbon dioxide) = 12.01 g/mol (molar mass of carbon) + (2 * 16.00 g/mol) (molar mass of oxygen) = 44.01 g/mol
- Molar mass of Cl2 (chlorine gas) = 35.45 g/mol (molar mass of chlorine) + 35.45 g/mol (molar mass of chlorine) = 70.90 g/mol
Now, let's calculate the ratio of the square roots of their molar masses:
√(molar mass of CO2) / √(molar mass of Cl2) = √(44.01 g/mol) / √(70.90 g/mol) ≈ 0.861
According to Graham's Law, the ratio of the rates of diffusion is equal to the inverse of the ratio of their square roots. Therefore, the ratio of the time taken by Cl2 gas to CO2 gas would be approximately equal to the inverse of the ratio we calculated:
1 / 0.861 ≈ 1.16
Since the time taken by CO2 gas to diffuse 5000 km is 2 seconds, we can find the time taken by Cl2 gas by multiplying it with the ratio:
2 seconds * 1.16 ≈ 2.32 seconds
Therefore, the time taken by Cl2 gas to diffuse the same distance of 5000 km would be approximately 2.32 seconds.